Problem $1$

Consider two concentric spherical regions:

A solid sphere $($inner sphere$)$ of radius $R_1$ with a non$-$uniform charge

density $(r)={}_0(\frac{r}{R_1}),$ where ${}_0$ is a constant, and $r$ is the distance

from the center.

A hollow spherical shell $($outer shell$)$ with inner radius $R_2$ and outer

radius $R_3,$ carrying a total charge $Q_2$ uniformly distributed over its

volume.

Determine the electric potential $V(r)$ at a distance $r$ from the center of the

spheres for the following regions:

$r{R}_1$

$r>R_3{R}_2$

$r>R_3{R}_1$

$R_2$

$r>R_3$